From 5cc58d1aa5bea519e790fd88a553bc6e5e99ad06 Mon Sep 17 00:00:00 2001
From: Michael Fogleman <fogleman@gmail.com>
Date: Sat, 20 Feb 2016 23:11:34 -0500
Subject: [PATCH] track current point; emulate cubic beziers

---
 README.md  |  2 +-
 bezier.go  | 32 +++++++++++++++++++++++++++++
 context.go | 59 ++++++++++++++++++++++++++++++++++++------------------
 point.go   | 11 ++++++++++
 4 files changed, 84 insertions(+), 20 deletions(-)
 create mode 100644 bezier.go
 create mode 100644 point.go

diff --git a/README.md b/README.md
index ec9bb52..dd3c57c 100644
--- a/README.md
+++ b/README.md
@@ -55,6 +55,7 @@ DrawImageAnchored(im image.Image, x, y int, ax, ay float64)
 MoveTo(x, y float64)
 LineTo(x, y float64)
 QuadraticTo(x1, y1, x2, y2 float64)
+CubicTo(x1, y1, x2, y2, x3, y3 float64)
 ClosePath()
 ClearPath()
 
@@ -132,7 +133,6 @@ even better, implement it and submit a pull request!
 
 - Clipping Regions
 - Gradients / Patterns
-- Cubic Beziers
 - Dashed Lines
 
 ## How Do it Do?
diff --git a/bezier.go b/bezier.go
new file mode 100644
index 0000000..1fcfd8c
--- /dev/null
+++ b/bezier.go
@@ -0,0 +1,32 @@
+package gg
+
+import "math"
+
+func cubic(x0, y0, x1, y1, x2, y2, x3, y3, t float64) (x, y float64) {
+	u := 1 - t
+	a := u * u * u
+	b := 3 * u * u * t
+	c := 3 * u * t * t
+	d := t * t * t
+	x = a*x0 + b*x1 + c*x2 + d*x3
+	y = a*y0 + b*y1 + c*y2 + d*y3
+	return
+}
+
+func CubicBezier(x0, y0, x1, y1, x2, y2, x3, y3 float64) []Point {
+	l := (math.Hypot(x1-x0, y1-y0) +
+		math.Hypot(x2-x1, y2-y1) +
+		math.Hypot(x3-x2, y3-y2))
+	n := int((l + 0.5))
+	if n < 4 {
+		n = 4
+	}
+	d := float64(n) - 1
+	result := make([]Point, n)
+	for i := 0; i < n; i++ {
+		t := float64(i) / d
+		x, y := cubic(x0, y0, x1, y1, x2, y2, x3, y3, t)
+		result[i] = Point{x, y}
+	}
+	return result
+}
diff --git a/context.go b/context.go
index 216c3a2..a66ebd9 100644
--- a/context.go
+++ b/context.go
@@ -9,7 +9,6 @@ import (
 	"github.com/golang/freetype/raster"
 	"golang.org/x/image/font"
 	"golang.org/x/image/font/basicfont"
-	"golang.org/x/image/math/fixed"
 )
 
 type LineCap int
@@ -41,7 +40,8 @@ type Context struct {
 	color      color.Color
 	strokePath raster.Path
 	fillPath   raster.Path
-	start      fixed.Point26_6
+	start      Point
+	current    Point
 	lineWidth  float64
 	lineCap    LineCap
 	lineJoin   LineJoin
@@ -170,12 +170,14 @@ func (dc *Context) SetRGB(r, g, b float64) {
 
 func (dc *Context) MoveTo(x, y float64) {
 	if len(dc.fillPath) > 0 {
-		dc.fillPath.Add1(dc.start)
+		dc.fillPath.Add1(dc.start.Fixed())
 	}
 	x, y = dc.TransformPoint(x, y)
-	dc.start = fp(x, y)
-	dc.strokePath.Start(dc.start)
-	dc.fillPath.Start(dc.start)
+	p := Point{x, y}
+	dc.strokePath.Start(p.Fixed())
+	dc.fillPath.Start(p.Fixed())
+	dc.start = p
+	dc.current = p
 }
 
 func (dc *Context) LineTo(x, y float64) {
@@ -183,29 +185,48 @@ func (dc *Context) LineTo(x, y float64) {
 		dc.MoveTo(x, y)
 	} else {
 		x, y = dc.TransformPoint(x, y)
-		p := fp(x, y)
-		dc.strokePath.Add1(p)
-		dc.fillPath.Add1(p)
+		p := Point{x, y}
+		dc.strokePath.Add1(p.Fixed())
+		dc.fillPath.Add1(p.Fixed())
+		dc.current = p
 	}
 }
 
 func (dc *Context) QuadraticTo(x1, y1, x2, y2 float64) {
 	if len(dc.strokePath) == 0 {
 		dc.MoveTo(x1, y1)
-	} else {
-		x1, y1 = dc.TransformPoint(x1, y1)
-		x2, y2 = dc.TransformPoint(x2, y2)
-		p1 := fp(x1, y1)
-		p2 := fp(x2, y2)
-		dc.strokePath.Add2(p1, p2)
-		dc.fillPath.Add2(p1, p2)
+	}
+	x1, y1 = dc.TransformPoint(x1, y1)
+	x2, y2 = dc.TransformPoint(x2, y2)
+	p1 := Point{x1, y1}
+	p2 := Point{x2, y2}
+	dc.strokePath.Add2(p1.Fixed(), p2.Fixed())
+	dc.fillPath.Add2(p1.Fixed(), p2.Fixed())
+	dc.current = p2
+}
+
+func (dc *Context) CubicTo(x1, y1, x2, y2, x3, y3 float64) {
+	if len(dc.strokePath) == 0 {
+		dc.MoveTo(x1, y1)
+	}
+	x0, y0 := dc.current.X, dc.current.Y
+	x1, y1 = dc.TransformPoint(x1, y1)
+	x2, y2 = dc.TransformPoint(x2, y2)
+	x3, y3 = dc.TransformPoint(x3, y3)
+	points := CubicBezier(x0, y0, x1, y1, x2, y2, x3, y3)
+	for _, p := range points[1:] {
+		f := p.Fixed()
+		dc.strokePath.Add1(f)
+		dc.fillPath.Add1(f)
+		dc.current = p
 	}
 }
 
 func (dc *Context) ClosePath() {
 	if len(dc.strokePath) > 0 {
-		dc.strokePath.Add1(dc.start)
-		dc.fillPath.Add1(dc.start)
+		dc.strokePath.Add1(dc.start.Fixed())
+		dc.fillPath.Add1(dc.start.Fixed())
+		dc.current = dc.start
 	}
 }
 
@@ -257,7 +278,7 @@ func (dc *Context) FillPreserve() {
 	if len(dc.fillPath) > 0 {
 		path = make(raster.Path, len(dc.fillPath))
 		copy(path, dc.fillPath)
-		path.Add1(dc.start)
+		path.Add1(dc.start.Fixed())
 	}
 	painter := raster.NewRGBAPainter(dc.im)
 	painter.SetColor(dc.color)
diff --git a/point.go b/point.go
new file mode 100644
index 0000000..cdbc2c8
--- /dev/null
+++ b/point.go
@@ -0,0 +1,11 @@
+package gg
+
+import "golang.org/x/image/math/fixed"
+
+type Point struct {
+	X, Y float64
+}
+
+func (p Point) Fixed() fixed.Point26_6 {
+	return fp(p.X, p.Y)
+}